Home > Algebra > Quadratic Functions and Their Graphs

How do you find the axis of symmetry, and the maximum or minimum value of the function #f(x)= x^2+2x-7#?

Answer 1

minimum at vertex (-1, -8)

x- coordinate of axis of symmetry, and of vertex: #x = -b/(2a) = -2/2 = -1# y-coordinate of vertex: f(-1) = 1 - 2 - 7 = - 8 Since a > 0, the parabola graph opens upward and has a minimum at vertex (-1, -8)

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Genesis Allen

To find the axis of symmetry, use the formula: x = -b / (2a), where a = coefficient of x^2, and b = coefficient of x.

For the function f(x) = x^2 + 2x - 7: a = 1 (coefficient of x^2) b = 2 (coefficient of x)

Axis of symmetry: x = -2 / (2 * 1) = -1

To find the maximum or minimum value, substitute the axis of symmetry into the function:

f(-1) = (-1)^2 + 2(-1) - 7 f(-1) = 1 - 2 - 7 f(-1) = -8

Since the coefficient of x^2 is positive, the parabola opens upwards, so the function has a minimum value at the vertex.

Minimum value: -8

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.