Consider the quadratic equation y = x² - 4x. If we graph the equation, where are the x-intercepts located? What is the x-coordinate of the vertex?

Q: 9. Identify the vertex, the y-intercept and the x intercepts for the following quadratic equation y…

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Q: Find the roots of the quadratic equation x + 2x - 3 = 0.

A: We will find the root by two methods first by splitting the middle term and second by discriminant…

Q: What is the axis of symmetry of the following quadratic equation? y = 2x +12x+10

A: Given,            y=2x2+12x+10To find : The axis of symmetry of the quadratic function.We know that,…

Q: The quantity b2 - 4ac is called the____ of a quadratic equation. If it is___, the equation has no…

A: We know ,for a quadratic equation of the form ax2+bx+c=0,(a≠0) Discriminant D is given by: D=b2-4ac…

Q: In a quadratic eqation(y=ax^2+bx+c) how does the change in values created in the a,b and c values…

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Q: write an equation of the parabola in intercept form x- intercepts of 12 and -6; passes through…

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Q: One root of the quadratic equation whose related function is graphed lies between which two…

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Q: Write an equation for the quadratic graphed below: x-intercepts: (-1,0) and (4,0); y-intercept:…

A: Given:- x-intercepts: (-1,0) and (4,0); y-intercept: (0,2) Graph          To find:- Write an…

Q: Write an equation for the quadratic graphed below x-intercepts: (-2,0) and (3,0). y-intercept: (0,1)

A: In general, y=a(x-h)2+k Where, (h,k)=vertex=(0,1) Then, the equation will be y=ax2+1

Q: Write an equation in standard form of the parabola that has the same shape as the graph of f(x) =…

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Q: Which of the following equations is a quadratic equation?

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Q: Write an equation for the quadratic graphed below I-intercepts: (-1,0) and (2,0). y-intercept: (0,1)…

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Q: If the discriminant of a quadratic equation is 4, then the equation has

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Q: The intercepts of the equation x2 + 4y2 = 16 are ________.

A: Given: x2 + 4y2 = 16

Q: If the quadratic functions for the equations are graphed, which is the widest? A) y= x2 B) y= 2x2 C)…

A: The graph shown in steps 2 , shows the graphs of above functions. Here, Red colour represents the…

Q: a. Solutions represent the the graph of a quadratic equation. of

A: Given : A quadratic equation

Q: If the zeros of a quadratic equation are -3 and 5, what would be the x-intercepts

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Q: A quadratic equation which goes

A: Given, a quadratic equation which goes through the origin has the form…

Q: Write an equation for the quadratic graphed below: x-intercepts: (-2,0) and (1,0); y-intercept:…

A: general equation of parabola :

Q: What is the axis of symmetry of the following quadratic equation? y= 2x-4x-5 O x = -1 O x = -5 O x =…

A: The given equation is: y=2x2-4x-5 The objective is to state the axis of symmetry of the given…

Q: The quantity b2 - 4ac is called the  _____________ of a quadratic equation. If it is _____________ ,…

A: To fill the blanks :   The quantity b2 - 4ac is called the _______ of  a quadratic equation. If…

Q: Solve the quadratic equation by finding the zeroes on your graphing calculator: 5x? - x - 4 = 0

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Q: Write an equation whose graph will have x-intercepts at the given values. 5 and -3 Complete the…

A: The given x intercepts are, 5 and -3

Q: 1. Solve by graphing  a) 3x - 2 = 2y   b) 5x-5y=10

A: See the attachment

Q: for the quadratic equation, state the axis of symmetry, vertex, and any intercepts. y=x^2-6x-7…

A: The objective is to solve the above question.

Q: Write an equation for the quadratic graphed below x-intercepts: (-2,0) and (1,0). y-intercept: (0,1)…

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Q: A player kicks the ball, and it travels according to the quadratic equation h(x) - -16x+40x where h…

A: Given h(x) = -16x2+40x Then (a) h'(x) = -32x+40 To find the critical point , put h'(x)=0 Consider…

Q: Find the intercepts of the graph of the equation y = x2 - 1x2 - 4

A: Given equation, y=x2-1x2-4                      ...(1)

Q: The discriminant of the quadratic equation 3x2 + 6x - 1 = 0 is [ Select ] and tells us that there…

A: we have to find the discriminant

Q: Find the standard equation for the quadratic function y = 3x² + 11x-4.

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Q: Write an equation for the quadratic graphed below x-intercepts: (-1,0) and (2,0). y-intercept:…

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Q: Which of the following quadratic equations contains the vertex (-5, 6) and has a y-intercept of (0,…

A: Given: - The vertex of the quadratic equation is, (-5,6) and has a y-intercept of (0,31) To find: -…

Q: If the discriminant of a quadratic equation is 0, then the equation has

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Q: What is the vertex of the quadratic equation below? y = -x² + 4x + 3 O (4, 3) O (3, 4) O (2, 7) O…

A: The quadratic function is given by y =-x2+4x+3 To evaluate : The vertex of the quadratic equation.

Q: When shifting right or left in a quadratic equation which term in ax^2+bx+c would you use?

A: The quadratic equation is ax2+bx+c

Q: Briefly discuss the effects of changing the values of a, h and k in the graph of quadratic…

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Q: Which is the vertex form of the equation for the quadratic function y = %3D 2x2 - 16x + 31?

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Q: Write an equation for the quadratic graphed below: x-intercepts: (-2,0) and (1,0); y-intercept:…

A: Equation of quadratic equation :

Q: Solve the equation 2x + 1 = x.+ 3 using the graph.

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Q: Write an equation for the quadratic graphed below: x-intercepts: (-3,0) and (2,0); y-intercept:…

A: the graph of the quadratic function is given: given that the x intercepts of the quadratic function…

Q: A bird taking a dive follows a path given by the quadratic equation y = 2x2 -5x. Solve the equation…

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Q: Write an equation in standard form of the parabola that has the same shape as the graph of f(x) =…

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Q: Graph the quadratic equation y = 10x² – 2x – 1 by creating a table of (x,y) values.

A: To plot the quadratic equation y=10x2-2x-1.

Q: Write an equation for the quadratic graphed below: x-intercepts: (-1,0) and (2,0); y-intercept:…

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Q: Write the Equation in standard form and sketch its graph. Show your solution. x² + 4x + 16y² – 128y…

A: Given the equation: x2+4x+16y2-128y+292=0

Q: If the discriminant of a quadratic equation is 2, then the equation has

A: The discriminant of a quadratic equation is given by b2-4ac We know that when the b2-4ac>0 then…

Q: Write an equation for the quadratic graphed below: x-intercepts: (-3,0) and (2,0); y-intercept:…

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Q: Use the graphical method to solve the equation.

A: Solution:Given   x-9-3x=0To solve the equation by using Graphical methd.

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.