How do you find the vertex and intercepts for #y = 4x^2 + 8x + 7#?
2 Answers
Therefore, the vertex is
Explanation:
Take out the common factor
Complete the square
Simplify
which is in the form
Therefore, the vertex is
For y-intercept, sub
For x-intercept, sub
Therefore, no solution as any number squared is greater than or equal to 0.
graph{4x^2+8x+7 [-10, 10, -5, 5]}
Above is the parabola
Vertex is at
y-intercept is at
(there is no x-intercept)
Explanation:
The easiest way (in this case) to find the vertex is to convert the given equation into vertex form:
Given
Extracting the
Completing the square:
Re-writing as a squared binomial and simplifying the constants
Adjusting the sign inside the squared binomial to match the vertex form requirement
which is the vertex form with vertex at
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The y-intercept is the value of
based on the original equation
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The x-intercept is the value of
from our derived vertex form:
but