Solve Quadratics by Graphing

Front

What is a quadratic equation?

Back

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

Front

What does it mean to solve a quadratic equation by graphing?

Back

Solving a quadratic equation by graphing involves plotting the quadratic function on a coordinate plane and identifying the points where the graph intersects the x-axis, which represent the solutions.

Front

What are the x-intercepts of a graph?

Back

The x-intercepts of a graph are the points where the graph crosses the x-axis, indicating the values of x for which the function equals zero.

Front

How can you find the vertex of a quadratic function?

Back

The vertex of a quadratic function in the form y = ax² + bx + c can be found using the formula x = -b/(2a). The y-coordinate can be found by substituting this x value back into the function.

Front

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

Back

The discriminant, given by the formula D = b² - 4ac, determines the nature of the roots of the quadratic equation: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Tags

CCSS.HSA-REI.B.4B

Front

What are the solutions of the equation x² + 12x + 35 = 0?

Back

The solutions are x = -5 and x = -7.

Tags

CCSS.HSA-REI.B.4B

Front

How do you solve the equation x² + 44 = -15x?

Back

Rearranging gives x² + 15x + 44 = 0. The solutions are x = -11 and x = -4.

Tags

CCSS.HSA-REI.B.4B

Front

What are the solutions of the graph that intersects the x-axis at -2 and 3?

Back

The solutions are x = -2 and x = 3.

Front

What are the solutions to the equation 3x² + 4x - 20 = 0?

Back

The solutions are x = -3.33 and x = 2.

Tags

CCSS.HSA-REI.B.4B

Front

What are the solutions of the equation x² - 6x + 8 = 0?

Back

The solutions are x = 2 and x = 4.

Tags

CCSS.HSA-REI.B.4B