Question

Graph the y = 2x ^ 2 - 12x + 15 Plot five points on the parabolathe vertextwo points to the left of the vertex, and two points to the right of the vertexThen click on the graph-a-function button

Answer 1

Explanation:

Given the function:

`y=2x^2-12x+15`

First, we find the vertex of the parabola.

Vertex

The equation of the axis of symmetry is calculated using the formula:

`x=-(b)/(2a)`

From the function: a=2, b=-12

`\implies x=-(-12)/(2(2))=(12)/(4)=3`

Substitute x=3 into y to find the y-coordinate at the vertex.

`\begin{gathered} y=2x^2-12x+15 \\ =2(3)^2-12(3)+15 \\ =18-36+15 \\ =-3 \end{gathered}`

The vertex is at (3, -3).

Two points to the left of the vertex

When x=2

`\begin{gathered} y=2x^2-12x+15 \\ =2(2)^2-12(2)+15=8-24+15=-1 \\ \implies(2,-1) \end{gathered}`

When x=1

`\begin{gathered} y=2x^2-12x+15 \\ =2(1)^2-12(1)+15=2-12+15=5 \\ \implies(1,5) \end{gathered}`

Two points to the right of the vertex

When x=4

`\begin{gathered} y=2x^2-12x+15 \\ =2(4)^2-12(4)+15=32-48+15=-1 \\ \implies(4,-1) \end{gathered}`

When x=5

`\begin{gathered} y=2x^2-12x+15 \\ =2(5)^2-12(5)+15=50-60+15=5 \\ \implies(5,5) \end{gathered}`

Answer:

Plot these points on the graph: (3, -3), (2,-1), (1,5), (4,-1), and (5,5).