Finding Zeros of Quadratics

Front

What is a zero of a quadratic function?

Back

A zero of a quadratic function is a value of x that makes the function equal to zero. It represents the x-intercepts of the graph.

Front

How do you find the zeros of the quadratic equation x^2 - 3x - 10?

Back

Factor the equation: (x - 5)(x + 2) = 0. The zeros are x = 5 and x = -2.

Front

What are the zeros of the quadratic equation x^2 + 5x - 14?

Back

The zeros are x = 2 and x = -7.

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.

Front

How do you factor the quadratic x^2 + x - 2?

Back

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

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, found at the point (h, k) in the vertex form y = a(x - h)² + k.

Front

What does the discriminant tell you about the roots of a quadratic equation?

Back

The discriminant (b² - 4ac) 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 axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror images, given by the formula x = -b/(2a).

Front

How can you verify if a number is a zero of a quadratic function?

Back

Substitute the number into the function. If the result is zero, then it is a zero of the function.

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.