8. (a) Find the vertex and the y-intercept of the parabola y = x²-4x+5. -8- -7 -6- 5 4- 3 2- 1- -4 -3 -2 -1 0 1 -1- -2 -3- -4- (b) On the set of axes at the right, draw the graph of the parabola of part (a). 2. 3 4 ·LO 5 -60- 7 8

Q: The parabola y = ² is changed to the form y = a (x − p)² + g by translating the parabola 2 units…

A: The parabola y=x2 is changed to the form y=ax-p2+q by translating the parabola 2 units down and 3…

Q: y= ax + c The vertex of the parabola in the xy-plane above is (0, c). Which of the following is true…

A:

Q: 3. Find the vertex for the parabola 4x + 2y² + 8 = 0. (a) (0, -2) (b) (-2,0) (c) (2, 2) (d) (-2,1)

A: The equation of the parabola is  4x+2y2+8=0

Q: 13. Which of the following is the equation of the graph shown? 2 Parabola Oy = - 3x? – 6x – 2 Oy = -…

A: The objective is to find the equation of the graph.

Q: 9. Find the vertex and focus of the parabola whose equation is 24x = -(y – 6)² + 192 O V(-8, –6),…

A:

Q: 25. Which equation represents the parabola below? 14 O y=4x² - 6x +17 Oy=x²-4x+5 OV-2X²-8X+9 y…

A: We know  Vertex form of parabola ⇒y=ax-h2+kHere vertexh,k

Q: Find the equation for the hyperbola whose graph is shown. -2 y 15 10 -10 -15 y=4x 2 y=-4x

A: Consider the graph

Q: ←+++ -10-9-8-7 Y 10- g 8+ 77 6 (0,3√5) 5+ 4+ 3+ -5- -7- -8+ 1 2 -6-(0,-3√5) -10- 3 4 5 ++ ++ x 6 7 8…

A:

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: Find the equation of the following parabola. Express your answer in standard form. 20 -15 -10 -5 15…

A: The standard equation of the parabola is written in the form ofy=ax2+bx+c

Q: If a parabola y=ax2+ky=ax2+k has vertex (0,−1)(0,−1) and passes through the point (4,2)(4,2). What…

A: A Parabola y=ax2+k       ...(1) has Vertex (0,-1) and Passes through the Point (4,2)

Q: 3) Explain how changing the a, h, and k variables affect the shape of the parabola in the vertex…

A: The vertex form of a parabola is given by y = a(x - h)² + k. In this equation, (h, k) is the vertex…

Q: Arrange the parabolas represented by the equations according to the positions of their foci on the…

A: The standard form of a parabola is  (x – h)2 = a(y – k) where (h, k) is the vertex.

Q: (-3,3) 76543 (-3,2) -6-5-4-3-2-1 -2 -3 4 2 3 4 5 6 7 (2, 4)

A: This is a downward parabola so vertex is the top most point on the parabola

Q: 10. Write the standard form of the equation of the parabola with vertex (5, -3), opens right, and…

A: Solution

Q: Graph the hyperbola. 2 9x²-y²=9 14 12- 10- (8-

A: Please refer to the image below l