Finding Zeros of Quadratics

Front

What are the zeros of a quadratic function?

Back

The zeros of a quadratic function are the values of x that make the function equal to zero. They are also known as the roots of the equation.

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

Front

How do you find the zeros of the quadratic equation x^2 - 2x - 24?

Back

To find the zeros, factor the equation: (x - 6)(x + 4) = 0. The zeros are x = 6 and x = -4.

Tags

CCSS.HSA-REI.B.4B

Front

What is the x-intercept of a function?

Back

The x-intercept is the point where the graph of the function crosses the x-axis, meaning the value of y is zero.

Front

How do you determine the x-intercepts of the function y = x^2 - 4?

Back

Set y = 0: 0 = x^2 - 4. Factor to get (x - 2)(x + 2) = 0. The x-intercepts are x = 2 and x = -2.

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

Front

What is the factored form of the quadratic x^2 + x - 2?

Back

The factored form is (x - 1)(x + 2).

Front

What does it mean for a quadratic to be factored?

Back

Factoring a quadratic means expressing it as a product of two binomials.

Front

What are the steps to factor a quadratic equation?

Back

1. Write the equation in standard form. 2. Find two numbers that multiply to the constant term and add to the coefficient of x. 3. Write the equation in factored form.

Front

What is the quadratic formula?

Back

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

Tags

CCSS.HSA-REI.B.4B

Front

How can you verify the zeros of a quadratic function?

Back

Substitute the zeros back into the original equation. If the result is zero, the values are correct.

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function.