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Elden [556K]
1 year ago
14

The equation of a quadratic is =2^2+3−2and after you factorizing 2^2+3−2=0you got x = -2 and x = 1/2 and the curve crosses the y

-axis at (0,-2)Using the information above, sketch the graph of =2^2+3−2
Mathematics
1 answer:
Lelechka [254]1 year ago
6 0

Given the next quadratic function:

y=2x^2+3x-2

to sketch its graph, first, we need to find its vertex. The x-coordinate of the vertex is found as follows:

x_V=\frac{-b}{2a}

where <em>a</em> and <em>b</em> are the first two coefficients of the quadratic function. Substituting with a = 2 and b = 3, we get:

\begin{gathered} x_V=\frac{-3}{2\cdot2} \\ x_V=-\frac{3}{4}=-0.75 \end{gathered}

The y-coordinate of the vertex is found by substituting the x-coordinate in the quadratic function, as follows:

\begin{gathered} y_V=2x^2_V+3x_V-2 \\ y_V=2\cdot(-\frac{3}{4})^2+3\cdot(-\frac{3}{4})-2 \\ y_V=2\cdot\frac{9}{16}+3\cdot(-\frac{3}{4})-2 \\ y_V=\frac{9}{8}-\frac{9}{4}-2 \\ y_V=-\frac{25}{8}=-3.125 \end{gathered}

The factorization indicates that the curve crosses the x-axis at the points (-2, 0) and (1/2, 0). We also know that the curve crosses the y-axis at (0,-2). Connecting these points and the vertex (-0.75, -3.125) with a U-shaped curve, we get:

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Answer:

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step 1 find a common denominator

common denominator - 8

* apply *

\frac{1^*^1}{8^*^8} =\frac{1}{8} \\\\\frac{1^*^4}{2^*^4} =\frac{4}{8} \\\\\frac{3^*^2}{4^*^2} =\frac{6}{8}

now we have

15\frac{1}{8} -3\frac{4}{8} -2\frac{6}{8}

step 2 make each fraction a improper fraction

We can do this my multiplying the big number by the denominator and adding that to the numerator.

15*8=120\\120+1=121\\\frac{121}{8} \\\\3*8=24\\24+4=28\\\frac{28}{8} \\\\2*8=16\\16+6=22\\\frac{22}{8}

now we have

\frac{121}{8} -\frac{28}{8} -\frac{22}{8}

Now we can subtract

remember when subtracting fractions you only subtract the numerators. ( so we keep the denominator as 8 )

so 121 - 28 - 22 = 71

so the answer is \frac{71}{8}

finally we want to change the answer back into a mixed fraction

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8 can go into 71 8 times

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3 years ago
After a party, Brendan had left over pizza. Brendan had one half of a cheese pizza, 3/4 of a sausage pizza, and 2/6 of a peppero
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3 years ago
Question #19- Use the answer bank below to fill in missing parts of the proof.
serious [3.7K]

Answer:

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3 years ago
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then with the zero product property, 0.5x can equal 0 and x would need to equal 0.
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