### About More on Parabolas:

When we work with quadratic equations, the vertex is not always obvious. We can complete the square and obtain vertex form. This form allows us to quickly gather the vertex. Alternatively, we can use the vertex formula. This formula allows us to quickly find the vertex when a quadratic equation is in standard form.

Test Objectives

- Demonstrate the ability to place a quadratic equation in vertex form by completing the square
- Demonstrate the ability to find the vertex using the vertex formula
- Demonstrate the ability to find the number of x-intercepts for a parabola

#1:

Instructions: Find the vertex by completing the square.

a) $$f(x) = 4x^2 + 2x + 6$$

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#2:

Instructions: Find the vertex by completing the square.

a) $$f(x) = -\frac{1}{3}x^2 + \frac{10}{3}x + \frac{10}{3}$$

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#3:

Instructions: Find the vertex using the vertex formula.

a) $$f(x) = -3x^2 + 24x - 54$$

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#4:

Instructions: Determine the number of x - intercepts.

a) $$f(x) = 10x^2 + 4x + 6$$

b) $$f(x) = 25x^2 + 30x + 9$$

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#5:

Instructions: Sketch the graph for each.

a) $$f(x) = -\frac{1}{4}x^2 - \frac{3}{2}x - \frac{5}{4}$$

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Written Solutions:

#1:

Solutions:

a) $$vertex: \left(-\frac{1}{4},\frac{23}{4}\right)$$

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#2:

Solutions:

a) $$vertex: \left(5,\frac{35}{3}\right)$$

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#3:

Solutions:

a) $$vertex: (4,-6)$$

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#4:

Solutions:

a) $$x-intercepts: \hspace{.25em} 0 $$

b) $$x-intercepts: \hspace{.25em} 1 $$

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#5:

Solutions:

a)