Answer: 5) Vertex = (2, 28) y-intercept = 40 → (0, 40)
6) Vertex = (2, 11) y-intercept = 7 → (0, 7)
Step-by-step explanation:
The y-intercept of the equation is when x = 0. It is the c-value when given in standard form: y = ax² + bx + c
To find the vertex, use the Axis of Symmetry equation to find the x-value
x = -b/(2a). Then plug the x-value into the equation to find the y-value.
5) y = 3x² - 12x + 40
↓ ↓ ↓
a=3 b= -12 c=40
[tex]\text{AOS:}\quad x=\dfrac{-b}{2a}\quad =\dfrac{-(-12)}{2(3)}\quad =\dfrac{12}{6}\quad =2[/tex]
Min: y = 3(2)² - 12(2) + 40
= 3(4) - 24 + 40
= 12 - 24 + 40
= 28
Vertex: (2, 28) y-intercept = 40
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6) y = -x² + 4x + 7
↓ ↓ ↓
a= -1 b=4 c=7
[tex]\text{AOS:}\quad x=\dfrac{-b}{2a}\quad =\dfrac{-(4)}{2(-1)}\quad =\dfrac{-4}{-2}\quad =2[/tex]
Max: y = -(2)² + 4(2) + 7
= -(4) + 8 + 7
= -4 + 8 + 7
= 11
Vertex: (2, 11) y-intercept = 7
