Question

Sketch the graph of these quadratics, labelling all significant points. Round the x-intercepts to

two decimal places.
a y = 2x2 + 8x - 5

Answer 1

See explanation

Explanation:

Given the quadratic function
`y=2x^2+8x-5`

To plot the graph of this function, find the vertex of parabola, x- and y- intercepts.

1. The vertex:

`x_v=(-b)/(2a)=(-8)/(2\cdot 2)=-(8)/(4)=-2\\ \\y_v=2\cdot (-2)^2+8\cdot (-2)-5=8-16-5=-13`

2. y-intercept:

`x=0\\ \\y=2\cdot 0^2+8\cdot 0-5=-5`

3. x-intercepts:

`y=0\\ \\2x^2+8x-5=0\\ \\D=b^2-4ac=8^2-4\cdot 2\cdot (-5)=64+40=104\\ \\√(D)=√(104)\approx 10.1980\\ \\x_(1,2)=(-b\pm√(D))/(2a)=(-8\pm 10.1980)/(2\cdot 2)\approx -4.55,\ 0.55`

4. The leading coefficient is 2 > 0, then parabola goes in positive y-direction