Test Review Quadratics

Front

What does h(10) = 0 signify in a quadratic function?

Back

It indicates that the value of the function h at x = 10 is zero, meaning (10, 0) is a point on the graph of the function where it intersects the x-axis.

Front

Calculate h(2) if h(x) = 3x^2 - 2x + 5.

Back

h(2) = 78.4.

Front

What is the value of f(-5) if f(x) = x^2 + 2x - 10?

Back

f(-5) = 3.

Front

Define a quadratic function.

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point on the graph of a quadratic function, depending on whether it opens upwards or downwards.

Front

How do you find the axis of symmetry for a quadratic function?

Back

The axis of symmetry can be found using the formula x = -b/(2a), where a and b are coefficients from the quadratic equation ax^2 + bx + c.

Front

What does it mean if a quadratic function has no real roots?

Back

It means the graph of the function does not intersect the x-axis, indicating that the discriminant (b^2 - 4ac) is less than zero.

Front

Explain the significance of the discriminant in a quadratic equation.

Back

The discriminant determines the nature of the roots of the quadratic equation: if it's positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

Front

What is the standard form of a quadratic equation?

Back

The standard form is written as ax^2 + bx + c = 0.

Front

How can you determine if a quadratic function opens upwards or downwards?

Back

If the coefficient 'a' in the quadratic function f(x) = ax^2 + bx + c is positive, it opens upwards; if 'a' is negative, it opens downwards.