Quadratic Equations

Front

What are the zeros of a quadratic function?

Back

The zeros of a quadratic function are the values of x for which the function equals zero. They can be found by factoring, using the quadratic formula, or graphing.

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

Front

What is the quadratic formula?

Back

The quadratic formula is given by x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are coefficients from the quadratic equation ax² + bx + c = 0.

Tags

CCSS.HSA-REI.B.4B

Front

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

Back

The y-intercept of a quadratic function is found by evaluating the function at x = 0. It is the point where the graph intersects the y-axis.

Tags

CCSS.HSF-IF.C.7A

Front

What does it mean if a quadratic equation has no real solutions?

Back

If a quadratic equation has no real solutions, it means that the discriminant (b² - 4ac) is less than zero, indicating that the graph does not intersect the x-axis.

Tags

CCSS.HSA-REI.B.4B

Front

How can you solve a quadratic equation by factoring?

Back

To solve a quadratic equation by factoring, express the equation in the form (x - p)(x - q) = 0, where p and q are the roots, and then set each factor equal to zero.

Tags

CCSS.HSA-REI.B.4B

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. It can be found using the formula (-b/(2a), f(-b/(2a))).

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. It can be found using the formula x = -b/(2a).

Front

What is the standard form of a quadratic equation?

Back

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

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots of the quadratic equation: if it's positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

Tags

CCSS.HSA-REI.B.4B

Front

How do you convert a quadratic equation from standard form to vertex form?

Back

To convert from standard form (ax² + bx + c) to vertex form (a(x - h)² + k), complete the square.