y = 2x^2 + 3x - 8y=2x2+3x−8
This equation is written in standard form, or y = ax^2 + bx + cy=ax2+bx+c
To find the xx-value of the vertex, or the axis of symmetry, we use the formula: x = -b/(2a)x=−b2a.
We know that a = 2a=2 and b = 3b=3, so we can plug in these values into the formula and solve:
x = -3/(2(2))x=−32(2)
x = -3/4x=−34
------------------−−−−−−−−−−−−−−−−−−
Now, to find the yy-value of the vertex, we just plug in the value of xx back into the original equation:
y = 2x^2 + 3x - 8y=2x2+3x−8
y = 2(-3/4)^2 + 3(-3/4) - 8y=2(−34)2+3(−34)−8
And now we simplify...
y = 2(9/16) - 9/4 - 8y=2(916)−94−8
y = cancel(2)color(red)1(9/(cancel(16)color(red)8)) - 9/4 - 8
y = 9/8 - 9/4 - 8
Make both fractions have the same denominator so you can subtract them:
y = 9/8 - 18/8 - 8
y = -9/8-8
Convert to mixed fraction form:
y = -1 1/8 - 8
y = -9 1/8
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Finally, the vertex is (-3/4, -9 1/8).
Hope this helps!
