Algebra 1: Graphing Quadratics Quiz

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Questions and Answers

Find the vertex of: y = 3(x - 9)^2 + 1

(9, -1)

Find the vertex of: y = -1(x + 9)^2 - 1

(-9, -1)

Find the vertex of: y = 4(x + 7)^2 + 8

(-7, 8)

Find the vertex of: y = -4(x + 8)^2 - 7

(-8, -7) Signup and view all the answers

Find the vertex of: y = 2(x - 3)^2 + 5

(3, 5) Signup and view all the answers

Find the vertex of: y = (x + 6)^2 - 2

(-6, -2) Signup and view all the answers

Find the vertex of: y = x^2 + 6x - 1

(-3, -10) Signup and view all the answers

Find the vertex of: y = x^2 - 4x + 3

(2, -1) Signup and view all the answers

Find the vertex of: y = 2x^2 + 4x - 10

(-1, -12) Signup and view all the answers

Find the vertex of: y = 3x^2 - 6x + 8

(1, 5) Signup and view all the answers

Find the y-intercept of: y = 5x^2 - 6x + 10

10 Signup and view all the answers

Find the y-intercept of: y = x^2 + 4x + 8

8 Signup and view all the answers

Find the y-intercept of: y = 3x^2 + 6x - 1

-1 Signup and view all the answers

Find the y-intercept of: y = 2(x + 1)^2 - 4

-2 Signup and view all the answers

Find the y-intercept of: y = -3(x - 4)^2 + 8

-40 Signup and view all the answers

Find the x-intercepts of: y = x^2 + 7x + 10

-7 & -2 Signup and view all the answers

Find the zeros of: y = x^2 + 9x - 10

-10 & 1 Signup and view all the answers

Find the roots of: y = x^2 - 7x + 12

4 & 3 Signup and view all the answers

Find the solutions of: y = x^2 - 8x - 20

10 & -2 Signup and view all the answers

Does the following quadratic open up or down? y = -4(x + 5)^2 + 10

False Signup and view all the answers

Does the following quadratic open up or down? y = 3x^2 + 9x - 1

False Signup and view all the answers

Study Notes

Vertex of Quadratic Functions

Vertex form of a quadratic equation is given by y = a(x - h)^2 + k, where (h, k) is the vertex.
The vertex is the highest or lowest point of the parabola, depending on the value of 'a'.
For y = 3(x - 9)^2 + 1, the vertex is (9, 1).
For y = -1(x + 9)^2 - 1, the vertex is (-9, -1).
For y = 4(x + 7)^2 + 8, the vertex is (-7, 8).
For y = -4(x + 8)^2 - 7, the vertex is (-8, -7).
For y = 2(x - 3)^2 + 5, the vertex is (3, 5).
For y = (x + 6)^2 - 2, the vertex is (-6, -2).
For quadratic in standard form y = x^2 + 6x - 1, the vertex can also be found at (-3, -10).
For y = x^2 - 4x + 3, the vertex is (2, -1).
For y = 2x^2 + 4x - 10, the vertex is (-1, -12).
For y = 3x^2 - 6x + 8, the vertex is (1, 5).

Y-Intercept of Quadratic Functions

The y-intercept is found by evaluating the function at x = 0.
For y = 5x^2 - 6x + 10, the y-intercept is 10.
For y = x^2 + 4x + 8, the y-intercept is 8.
For y = 3x^2 + 6x - 1, the y-intercept is -1.
For y = 2(x + 1)^2 - 4, the y-intercept is -2.
For y = -3(x - 4)^2 + 8, the y-intercept is -40.

X-Intercepts & Roots of Quadratic Functions

X-intercepts are found where y = 0, which gives the roots of the quadratic.
For y = x^2 + 7x + 10, the roots are -7 and -2.
For y = x^2 + 9x - 10, the roots are -10 and 1.
For y = x^2 - 7x + 12, the roots are 4 and 3.
For y = x^2 - 8x - 20, the solutions are 10 and -2.

Orientation of Parabolas

A quadratic opens upwards if 'a' is positive and downwards if 'a' is negative.
For y = -4(x + 5)^2 + 10, the parabola opens down.
For y = 3x^2 + 9x - 1, the parabola opens up.

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Description

Test your understanding of graphing quadratics by finding the vertex of given functions. This quiz focuses on both vertex and standard form equations. Improve your algebra skills with these practice questions.