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
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Find the vertex of: y = 2(x - 3)^2 + 5
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Find the vertex of: y = (x + 6)^2 - 2
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Find the vertex of: y = x^2 + 6x - 1
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Find the vertex of: y = x^2 - 4x + 3
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Find the vertex of: y = 2x^2 + 4x - 10
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Find the vertex of: y = 3x^2 - 6x + 8
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Find the y-intercept of: y = 5x^2 - 6x + 10
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Find the y-intercept of: y = x^2 + 4x + 8
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Find the y-intercept of: y = 3x^2 + 6x - 1
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Find the y-intercept of: y = 2(x + 1)^2 - 4
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Find the y-intercept of: y = -3(x - 4)^2 + 8
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Find the x-intercepts of: y = x^2 + 7x + 10
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Find the zeros of: y = x^2 + 9x - 10
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Find the roots of: y = x^2 - 7x + 12
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Find the solutions of: y = x^2 - 8x - 20
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Does the following quadratic open up or down? y = -4(x + 5)^2 + 10
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Does the following quadratic open up or down? y = 3x^2 + 9x - 1
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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.
