Unit 4b Make-Up Test Review (up to 50%)

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is given by f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How do you find the value of 'a' in the vertex form of a parabola?

Back

To find 'a', use a point on the parabola (x, y) and substitute it into the vertex form equation f(x) = a(x - h)² + k, then solve for 'a'.

Front

What does the vertex of a parabola represent?

Back

The vertex of a parabola represents the highest or lowest point of the graph, depending on whether it opens upwards or downwards.

Front

How can you determine if a parabola opens upwards or downwards?

Back

A parabola opens upwards if 'a' > 0 and downwards if 'a' < 0 in the vertex form f(x) = a(x - h)² + k.

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = h, where (h, k) is the vertex.

Front

What are the zeros of a quadratic function?

Back

The zeros of a quadratic function are the x-values where the graph intersects the x-axis, also known as the roots of the equation.

Front

How do you find the zeros of a quadratic equation in standard form?

Back

To find the zeros of a quadratic equation in standard form ax² + bx + c = 0, use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

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

Back

The discriminant (b² - 4ac) determines the nature of the roots: if > 0, two distinct real roots; if = 0, one real root; if < 0, no real roots.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

How can you convert a quadratic equation from standard form to vertex form?

Back

To convert from standard form to vertex form, complete the square on the quadratic expression.