Question

Write the standard form of the quadratic function whose graph is a parabola with the given vertex and that passes through the given point. (Let x be the independent variable and y be the dependent variable.) Vertex: (−4, 8); point: (0, 24)

Answer 1

y = x² + 8x + 24

Explanation:

The standard form of the quadratic function whose graph is a parabola with the given vertex and that passes through the given point is;

y = x² + 8x + 24

The question gives us:

Vertex coordinate; (-4, 8)

A point on the graph; (0, 24)

The vertex form of a quadratic equation is given by;

y = a(x - h)² + k, where (h, k) are the coordinates of the vertex.

And a is the letter in general form of quadratic equation which is;

y = ax² + bx + c

Thus, at point (0, 24) at the vertex of (-4, 8), we have;

24 = a(0 - (-4))² + 8

24 = a(4)²+8

24 - 8 = 16a

16a = 16

a = 16/16

a = 1

Since y = a(x - h)² + k is the vertex form, let us put the vertex values for h and k as well as the value of a to get the quadratic equation;

y = 1(x - (-4))² + 8

y = x² + 8x + 16 + 8

y = x² + 8x + 24