Solutions to Quadratic Equations

Front

How many solutions can a quadratic equation have?

Back

A quadratic equation can have 0, 1, or 2 solutions.

Front

What is another name for the x-intercepts of a quadratic equation?

Back

Zeros.

Tags

CCSS.HSF-IF.C.7C

Front

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

Back

The graph of the quadratic does not intersect the x-axis.

Front

What does it mean if a quadratic equation has one solution?

Back

The graph of the quadratic touches the x-axis at one point (the vertex).

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 quadratic function?

Back

The vertex is the highest or lowest point on the graph of the quadratic.

Front

How can you determine the number of solutions from the graph of a quadratic?

Back

Count the number of times the graph intersects the x-axis.

Front

What is the quadratic formula used for?

Back

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

Tags

CCSS.HSA-REI.B.4B

Front

What does the discriminant (b² - 4ac) tell us about a quadratic equation?

Back

The discriminant indicates the number of solutions: if > 0, two solutions; if = 0, one solution; if < 0, no real solutions.

Tags

CCSS.HSA-REI.B.4B

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 x = -b/(2a).