find the equation of the parabola y = ax? + bx + c that passes through the points. (0, 3), (1, 4), (2, 3)

Q: What is the turning point of the parabola whose equation is y = 2x2 + 4x- 3? А (1,3) С 2, 13) 8…

A: The turning point is the vertex.  The formula is   -b2a given equation y=2x2+4x-3compare the…

Q: Find the coordinates of the vertex of the parabola y = x^2 - 4x + 1 using derivatives O (2, -3) O…

A: To find the vertex of the parabola by using derivatives

Q: Find the equation of the parabola, y = ax^2 + bx + c, that passes through the points (0,5), (2,-5),…

A: we have to find the equation of the parabola y=ax2+bx+c that passes through the points (0,5), (2,-5)…

Q: Find the intersection points of the parabola above and the line -x+y=-4.

A: Given equation of parabola and the line are as below.

Q: What are the coordinates for the vertex of the parabola y = 3x2 - 6x- 1? O (1,-4) O (1,4) 0(-1,4)…

A: answer is option A.)   explanation is given in below step

Q: Find the point on the parabola x= - 2t, y = - 2t, - o <t< oo, closest to the point (- 32, – 1).

A: Let the point (x, y)=(-2t, -2t2) on the parabola be the closest point to (-32, -1) So distance…

Q: Write the standard form of the equation of the parabola that has the indicated vertex and passes…

A: To write the standard form of the equation of the parabola that has the vertex at the point 1, -4…

Q: Find the equation of the parabola whose axis is parallel to the x-axis and passes through the points…

A: We will find out the required value.

Q: What is the equation in vertex form of a parabola with a vertex of (-3, 4) that passes through the…

A:

Q: Find the standard equation of any parabola that has vertex V.

A: The equation is a statement that consists of equal symbol between two algebraic expressions. The…

Q: What is the equation of the parabola containing the points (0, 5), (–1,9), and (2, 3)? O y = r-z+5 O…

A: The standard form of a parabola is y=ax2+bx+c. The required parabola passes through the 3 points are…

Q: Find an equation for the parabola that has a horizontal axis and passes through the given…

A:

Q: Find the equation y=ax^2+bx+c of the parabola that passes through the points (-2, 0), (0, -14), (7,…

A:

Q: Find the equation of the parabola, y=ax^2 + bx + c, that passes through the points (1,4), (-1,0),…

A:

Q: Find the vertex of the parabola. y = 3x² - 1 О (0, (0, –1) O (-1, 3) O (-1, 0) (3, –1) (0, 3)

A: topic - parabola

Q: What are the coordinates of the turning 6) point of the parabola whose equation is y = x2 - 2x - 4?…

A: Turning point of parabola is the vertex of parabola .  General equation of parabola :  y = (x - h)2…

Q: Find the equation of the parabola y = ax? + bx + c passing through the points (0, 6), (- 2, 2), and…

A:

Q: Find b and c so that the parabola with equation y = 4x2 - bx - c has a vertex at (2 , 4)?

A: Using the vertex formula we find the x value of the vertex[formula: x value of vertex of Ax^2+Bx+C=0…

Q: Give 3 points that lie on the parabola y=x^2-5x-2

A:

Q: Find the equation y=ax2+bx+c of the parabola that passes through the points (-2,0), (0,-14), (7,0)

A: The equation is:-

Q: Which is the equation of a parabola that has x-intercepts at (2,0) and (-6, 0)?

A:

Q: Find the equation y = ax2 + bx + c of the parabola that passes through the points (-2,0), (0, –14),…

A: See attached file for a step by step explanation to find the equation of parabola.

Q: Find the equation of the plane perpendicular to the y-axis and passing through the point (3,2,-2)

A:

Q: Find the coordinates of the point on the parabola y = x² which is closest to the point (3, 0).

A:

Q: What is the equation of the parabola below? (4,3) -5 5. (2.-1) -5- A) y 2(x + 2)2 + 1 B) y 2(x- 2)2-…

A:

Q: Find an equation of the parabola with vertex (3, 4) and directrix y = 1.

A: Graph of parabola :

Q: Write the standard form of the equation of the parabola that has the indicated vertex and passes…

A: Given information: The vertex of the parabola is 2,-4 and the points is -2,44. Calculation: The…

Q: 5) Find the equation for the parabola that has its vertex at (5,-3), axis parallel to the y-axis,…

A: given,         vertex of parabola =5,-3  and passing through the point 9,5

Q: What is the equation of the line that contains the vertices of the hyperbola (x + 4)² (y + 2)² -1? 9…

A: Finding the vertices

Q: 2. Write the general equation of the parabola with directrix at x FG,-1), and v (. -1). 2

A:

Q: (3) Find the coordinates of the points of intersection of the parabola y = x2 - ax and the line y =…

A:

Q: Find the point on the parabola (y = x2/2) that is closest to the point (-4,1)

A: Use distance formula to evaluate

Q: How do I solve this optimization problem?

A:

Q: What is the equation of the given parabola? y 4 -5-4-3-2 1 2 3 4 5 A y= 3x² 6x +3 I23 45

A: Here zeros form equation y=a(x-p)(x-q) p,q are zeros of equation

Q: What point on the parabola y = 6 – x is closest to the point (6,6)?

A:

Q: Which conic section is represented by the equation 2x2 + 4x - y+9= 0?

A:

Q: Find an equation of the paranola in standard form: with the vertex at V (2,-4) and directrix y= -5

A: Find an equation of the parabola in standard form: with the vertex at V (2,-4) and directrix y= -5

Q: A parabola with the equation y = -2x + 4x +3 is intersected by a line with a slope of 1 that passes…

A: First of all we will find the equation of the straight line and then equate the two curves to find…

Q: What is the standard equation of the parabola which satisfies the following properties: V(-4,2),…

A: Let's find.

Q: Write the standard form of the equation of the parabola that has the indicated vertex and passes…

A: GIven information: The vertex of the parabola is -3,4 and the point is 0,13. The general equation of…

Q: d. Find the equation of the vertical parabola that passes through the points: A = (6, 1), B = (-2,…

A:

Q: If we have a parabola with an axis of symmetry of x = 9 and it contains the point (-3, -12), what…

A: Given taht parabola is symmetric about the line x= 9

Q: Find the equation of the parabola y = ax^2 + bx +c that passes through the points (-1,-4) (1,4), and…

A: topic  -  parabola

Q: Find the Equation of a Quadratic (Parabola) Given 3 Points y=a^2+bx+c (0,0), (-3,3), (3,3) Also,…

A:

Q: Find the equation of the line tangent to (a) The parabola z = 2x² - 3y², y = 1 at the point (-2,1,5)…

A: Given: we have to find equation of tangent lines   equation of tangent line : y-y1=m(x-x1)

Q: Find the point(s) on the ellipse 4x² + y² = 4 that are farthest from the point (1,0).

A: We need to find the points on the ellipse that is farthest from the given point. According to first…

Q: Write an equation of the parabola in intercept form. 14. x-intercepts of 3 and -4; passes through…

A: equation of the parabola in intercept form is given below- y=a*(x-p)*(x-q) where p,q are intercepted…