Graphing Quadratics using x-intercepts

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts of a quadratic function are the points where the graph intersects the x-axis, which occur when f(x) = 0.

Front

How do you find the y-intercept of a quadratic function?

Back

The y-intercept of a quadratic function can be found by evaluating the function at x = 0, which gives the point (0, f(0)).

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola (opening upwards or downwards).

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-image halves, given by the equation x = -b/(2a).

Front

What does the 'a' value in a quadratic function indicate?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c.

Front

What is the factored form of a quadratic function?

Back

The factored form of a quadratic function is f(x) = a(x - r1)(x - r2), where r1 and r2 are the roots or x-intercepts.

Front

How can you determine the number of x-intercepts of a quadratic function?

Back

The number of x-intercepts can be determined using the discriminant (b² - 4ac) from the quadratic formula. If it's positive, there are 2 intercepts; if zero, 1 intercept; if negative, none.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the x-intercepts of a quadratic function.