Solving Quadratics

Front

What are the roots of the function f(x)= (x - 2)(x + 3)?

Back

x = 2 or x = -3

Front

A parabola has a vertex at (-3,2). Where is the axis of symmetry?

Back

x = -3

Front

Write y = x^2 - 18x + 52 in vertex form.

Back

y = (x - 9)^2 - 29

Front

Graph the quadratic function y = 2x^2 + 8x + 6. What is the y-intercept of the parabola?

Back

6

Front

What is the green dashed line called?

Back

axis of symmetry

Front

What is the standard form of a quadratic equation?

Back

y = 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

Use the formula x = -b/(2a) to find the x-coordinate, then substitute back to find the y-coordinate.

Front

What is the discriminant in a quadratic equation and what does it indicate?

Back

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

Front

What is the vertex of the parabola given by the equation y = 3(x - 2)^2 + 5?

Back

The vertex is (2, 5).

Front

What does the 'a' value in the quadratic equation y = ax^2 + bx + c 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.