Solving Quadratics

Front

What are the zeros of a quadratic equation?

Back

The zeros of a quadratic equation are the values of x that make the equation equal to zero. They can be found by factoring, using the quadratic formula, or completing the square.

Front

How do you find the zeros of the equation (x+10)(x-2) = 0?

Back

Set each factor equal to zero: x + 10 = 0 (x = -10) and x - 2 = 0 (x = 2). The zeros are -10 and 2.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions (zeros) of a quadratic equation ax² + bx + c = 0.

Front

Solve the equation 3x² - 192 = 0.

Back

x = -8 or x = 8.

Front

What does it mean to solve a quadratic equation?

Back

To solve a quadratic equation means to find the values of x that satisfy the equation, typically resulting in the zeros of the function.

Front

What are the steps to solve a quadratic equation by factoring?

Back

1. Write the equation in standard form (ax² + bx + c = 0). 2. Factor the quadratic expression. 3. Set each factor equal to zero. 4. Solve for x.

Front

What is the vertex of a parabola?

Back

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

Front

Solve the equation a² + 2a - 24 = 0.

Back

a = -6 or a = 4.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root (b² - 4ac) that determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

Front

Solve the equation 4m² - 100 = 0.

Back

m = 5 or m = -5.