Quadratics - 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

How does the value of 'a' in the vertex form affect the graph of the parabola?

Back

The value of 'a' determines the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards. A larger absolute value of 'a' makes the parabola narrower.

Front

What does the term (x - h) represent in the vertex form?

Back

The term (x - h) represents a horizontal translation of the graph. If h is positive, the graph shifts to the right; if h is negative, it shifts to the left.

Front

What does the term + k represent in the vertex form?

Back

The term + k represents a vertical translation of the graph. If k is positive, the graph shifts up; if k is negative, it shifts down.

Front

Given the equation y = (x - 3)² + 2, what is the vertex of the parabola?

Back

The vertex of the parabola is (3, 2).

Front

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

Back

To find the vertex of a parabola in vertex form y = a(x - h)² + k, identify the values of h and k. The vertex is (h, k).

Front

What is the effect of translating the graph of y = x² to the right by 4 units?

Back

The new equation will be y = (x - 4)², which shifts the vertex from (0, 0) to (4, 0).

Front

If the equation of a parabola is y = (x + 2)² - 3, what is the translation from the parent function y = x²?

Back

The graph is translated left 2 units and down 3 units.

Front

What is the parent function of a quadratic equation?

Back

The parent function of a quadratic equation is y = x².

Front

How do you determine the direction in which a parabola opens?

Back

The direction in which a parabola opens is determined by the coefficient 'a' in the vertex form. If 'a' > 0, it opens upwards; if 'a' < 0, it opens downwards.