How do you find the vertex of the quadratic equation [tex]m^2 - 5m - 14 = 0[/tex]?
Answer (2)
To find the vertex of a quadratic equation m 2 − 5 m − 14 = 0 ,[/tex] use ( m = \frac{-b}{2a} \). Substitute to get \( m = \frac{5}{2} \). The corresponding y \) value is \( -\frac{81}{4} \
To find the vertex of a quadratic equation in the form ax^2 + bx + c = 0 \ you can use the formula:
x = − 2 a b
For the equation m^2 - 5m - 14 = 0 \ the coefficient of m^2 \) is \( a = 1 \)and the coefficient of\( m \) is \( b = -5 \
Using the formula, we get:
m = − 2 ( 1 ) − 5
m = 2 5
Now, to find the corresponding value of m \ substitute [tex] m = 2 5 into the quadratic equation:
m 2 − 5 m − 14 = ( 2 5 ) 2 − 5 ( 2 5 ) − 14
m 2 − 5 m − 14 = 4 25 − 2 25 − 14
m 2 − 5 m − 14 = 4 25 − 4 50 − 14
m 2 − 5 m − 14 = − 4 25 − 14
m 2 − 5 m − 14 = − 4 25 − 4 56
m 2 − 5 m − 14 = − 4 81
So, the vertex of the quadratic equation m 2 − 5 m − 14 = 0 is at m = \frac{5}{2} \) and \( -\frac{81}{4} \
To find the vertex of the quadratic equation m 2 − 5 m − 14 = 0 , we calculate the x-coordinate using the formula m = − 2 a b , giving us m = 2 5 . The corresponding y-coordinate is found by substituting m = 2 5 back into the equation, resulting in the vertex at ( 2 5 , − 4 81 ) .
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