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Flauer [41]
1 year ago
11

100 POINTS please show your work

Mathematics
1 answer:
Anon25 [30]1 year ago
8 0

Answer:

See below for answers and explanations (along with a graph)

Step-by-step explanation:

<u>Part A</u>

Set f(x)=0 and factor the expression by grouping:

f(x)=2x^2-3x-5\\\\0=2x^2-3x-5\\\\0=2x^2+2x-5x-5\\\\0=2x(x+1)-5(x+1)\\\\0=(2x-5)(x+1)

Use the Zero Product Property to find the x-intercepts:

0=2x-5\\5=2x\\x=\frac{5}{2}

0=x+1\\x=-1

Hence, the x-intercepts for the graph of f(x) are x=-1 and x=\frac{5}{2}.

<u>Part B</u>

Find the x-coordinate of the vertex:

x=-\frac{b}{2a}\\ \\x=-\frac{(-3)}{2(2)}\\\\x=\frac{3}{4}

Find the y-coordinate of the vertex:

f(\frac{3}{4})=2(\frac{3}{4})^2-3(\frac{3}{4})-5=-\frac{49}{8}

Hence, the vertex is (\frac{3}{4},-\frac{49}{8}). We can see from the positive leading coefficient of the function that the vertex will be a minimum because the parabola will open faced-up.

<u>Part C</u>

You can use the x-intercepts and vertex to plot points of the graph of the function. Additionally, you can throw in the y-intercept in as well. The y-intercept, in this case, is f(0)=2(0)^2-3(0)-5=-5, or (0,-5) as an ordered pair. See attached graph.

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