Question

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

he given point. (Let x be the independent variable and y be the dependent variable.)
Vertex: (-4, 9); point: (0,25)
y = (x-4)² +1

Answer 1

The equation of the quadratic function is y = (x + 4)² + 9.

Step-by-step explanation:

The standard form of a quadratic function is given by y = ax² + bx + c, where a, b, and c are constants. To find the equation of the quadratic function, we can substitute the vertex coordinates (-4, 9) into the standard form. This gives us:

y = a(x - (-4))² + 9

y = a(x + 4)² + 9

Now, we can substitute the point (0, 25) into the equation:

25 = a(0 + 4)² + 9

25 = a(4)² + 9

25 = 16a + 9

16a = 25 - 9

16a = 16

a = 1

Substituting the value of a = 1 back into the equation, we get:

y = (x + 4)² + 9

Learn more about Standard form of quadratic function