Question

Find the vertex and y intercept of the quadratic function​

Answer 1

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

$\text{AOS:}\quad x=\dfrac{-b}{2a}\quad =\dfrac{-(-12)}{2(3)}\quad =\dfrac{12}{6}\quad =2$

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

$\text{AOS:}\quad x=\dfrac{-b}{2a}\quad =\dfrac{-(4)}{2(-1)}\quad =\dfrac{-4}{-2}\quad =2$

Max:  y = -(2)² + 4(2) + 7

           = -(4)  + 8 + 7

           = -4 + 8 + 7

           = 11

Vertex: (2, 11)    y-intercept = 7