Solve Quadratics by Graphing

Front

What does it mean if the graph of a quadratic does not intercept the x-axis?

Back

It has no real solutions.

Front

How do you solve the quadratic equation 2x² + 17x + 21 = 0?

Back

By factoring or using the quadratic formula, the solutions are x = -7 and x = -3/2.

Tags

CCSS.HSA-REI.B.4B

Front

What are the x-intercepts of a quadratic function?

Back

They are the points where the graph intersects the x-axis, also known as the zeros of the function.

Tags

CCSS.HSF-IF.C.7A

Front

What is the formula to find the Axis of Symmetry of a quadratic function?

Back

The Axis of Symmetry can be found using the formula x = -b/(2a), where a and b are coefficients from the quadratic equation ax² + bx + c.

Front

How many zeros can a parabola have?

Back

A parabola can have 0, 1, or 2 zeros.

Tags

CCSS.HSF-IF.C.7A

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.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

How can you determine if a quadratic opens upwards or downwards?

Back

If the coefficient 'a' in the standard form ax² + bx + c is positive, it opens upwards; if 'a' is negative, it opens downwards.

Tags

CCSS.HSF-IF.C.7A

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac, which determines the nature of the roots.

Tags

CCSS.HSA-REI.B.4B

Front

What does a positive discriminant indicate about the roots of a quadratic equation?

Back

It indicates that there are two distinct real roots.

Tags

CCSS.HSA-REI.B.4B