Algebra 2 CP Vertex and Intercept Forms

Questions and Answers

What is the vertex form equation?

y = a(x-h)² + k

What are the steps for using vertex form instructions? (Select all that apply)

State vertex (h,k) (correct)

Find y-intercept by letting x = 0 (correct)

Use the quadratic formula

Find x-intercepts by using the square root method (correct)

What is the intercept form equation?

y = a(x-p)(x-q)

What are the steps for using intercept form instructions? (Select all that apply)

Find the vertex by finding the midpoint of x-int values Signup and view all the answers

What is the standard form equation?

y = ax² + bx + c Signup and view all the answers

What are the steps for using standard form instructions? (Select all that apply)

Find x-intercepts by letting y = 0 Signup and view all the answers

Study Notes

Vertex Form

Equation: ( y = a(x-h)^2 + k ) where (h, k) is the vertex.
Vertex is found by setting the parentheses ( (x-h) ) equal to zero to find ( h ); ( k ) remains unchanged.
To find x-intercepts, set ( y = 0 ) and use the square root method.
Y-intercept is determined by substituting ( x = 0 ) into the equation.
Utilize the x-value from the vertex to identify additional points on the graph.

Intercept Form

Equation: ( y = a(x-p)(x-q) ) where p and q are x-intercepts.
To find x-intercepts, set each factor equal to zero.
The vertex is calculated by finding the midpoint between p and q, then substituting this x-value back into the equation for the corresponding y-coordinate.
Y-intercept is found by plugging ( x = 0 ) into the equation.
The x-value from the vertex can also be used to identify further graph points.

Standard Form

Equation: ( y = ax^2 + bx + c ).
Vertex is located at ( \left(-\frac{b}{2a}, y\right) ); y is found by substituting the x-value into the equation.
Axis of symmetry is represented by the x-value from the vertex.
X-intercepts are found by setting ( y = 0 ) and solving using factoring or the quadratic formula.
Y-intercept is obtained by substituting ( x = 0 ) into the equation.
The x-value from the vertex aids in locating additional points on the graph.

Description

This quiz covers the vertex and intercept forms of quadratic equations as instructed in Algebra 2 CP. It includes definitions, equations, and step-by-step instructions for solving problems related to these forms. Test your understanding of the concepts and improve your algebra skills.