Quadratics Review Pt.1

Front

What is the axis of symmetry for a parabola with vertex at (-3, 2)?

Back

The axis of symmetry is the vertical line that passes through the vertex. For the vertex (-3, 2), the axis of symmetry is given by the equation x = -3.

Front

What is the maximum height of the ball represented by the function y = -\frac{1}{2}x^2 + 2x + 2?

Back

The maximum height of the ball is 4 feet, which occurs at the vertex of the parabola.

Front

Back

Front

What are the zeros of the function f(x) = 2x^2 - 3x - 5?

Back

Front

Convert the quadratic function f(x) = 4x^2 - 32x + 2 to vertex form.

Back

The vertex form is f(x) = 4(x - 4)^2 - 62.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

How do you find the vertex of a parabola given in standard form?

Back

The vertex (h, k) can be found using the formula h = -\frac{b}{2a} and k = f(h).

Front

What does the 'a' value in a quadratic function determine?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

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, the parabola opens upwards; if negative, it opens downwards.