Week 16 Flashcard Graphing Quadratics in Vertex Form

Front

What is the vertex form of a quadratic equation?

Back

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

Front

What does the 'a' value in the vertex form indicate?

Back

The 'a' value determines the direction of the parabola's opening: if 'a' is positive, it opens upward; if 'a' is negative, it opens downward.

Front

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

Back

The vertex can be found directly from the vertex form y = a(x - h)² + k, where the vertex is (h, k).

Front

What is the axis of symmetry in a quadratic function?

Back

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

Front

How do you determine the y-intercept of a quadratic function?

Back

The y-intercept can be found by setting x = 0 in the quadratic equation and solving for y.

Front

What is the significance of the zeros of a quadratic function?

Back

The zeros (or roots) of a quadratic function are the x-values where the graph intersects the x-axis, indicating the solutions to the equation.

Front

How can you determine the number of zeros a quadratic function has?

Back

The number of zeros can be determined using the discriminant (b² - 4ac) from the standard form of the quadratic equation. If it's positive, there are 2 zeros; if zero, 1 zero; if negative, no zeros.

Front

What transformation shifts the graph of y = x² to the right by 3 units?

Back

The transformation is y = (x - 3)².

Front

What transformation shifts the graph of y = x² down by 5 units?

Back

The transformation is y = x² - 5.

Front

What is the effect of multiplying a quadratic function by a number greater than 1?

Back

Multiplying by a number greater than 1 vertically stretches the graph of the parabola.