Help please 1 thought 3
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Answer:
The zeros are x = -1 and x = 8
The vertex is (3.5, -20.25)
Step-by-step explanation:
When we have a quadratic equation like:
y = a*x^2 + b*x + c
The zeros of the function are the values of x such that:
a*x^2 + b*x + c = 0
And the solutions are given by the Bhaskara's equation, which is:
And the vertex is at:
x = -b/2a
The y-value at the vertex is the function evaluated in that point.
In this case, we have the equation:
h(x) = x^2 - 7*x - 8
Then:
a = 1
b = -7
c= -8
Replacing these in the Bhaskara's equation we get:
Then the two solutions are:
x = (7 - 9)/2 = -2/2 = -1 (this is the smaller one)
and
x = (7 + 9)/2 = 16/2 = 8 (this is the larger one)
And we will have the vertex at:
x = -(-7)/2*1 = 7/2 = 3.5
Evaluating h(x) in 3.5 we get:
h(3.5) = (3.5)^2 - 7*(3.5) - 8 = -20.25
Then the vertex is the point:
(3.5, -20.25)