Question

Consider the quadratic function f(x) = 2x2 – 8x – 10. The x-component of the vertex is . The y-component of the vertex is . The discriminant is b2 – 4ac = (–8)2 – (4)(2)(–10) = .

Answer 1

Answer:

2

-18

144

Step-by-step explanation:

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Answer 2

Answer:

Part 1) The x-component of the vertex is 2 and the y-component of the vertex is -18

Part 2) The discriminant is 144

Step-by-step explanation:

we have

$f(x)=2x^{2}-8x-10$

step 1

Find the discriminant

The discriminant of a quadratic equation is equal to

$D=b^{2}-4ac$

in this problem we have

$f(x)=2x^{2}-8x-10$

so

$a=2\\b=-8\\c=-10$

substitute

$D=(-8)^{2}-4(2)(-10)$

$D=64+80=144$

The discriminant is greater than zero, therefore the quadratic equation has two real solutions

step 2

Find the vertex

Convert the quadratic equation into vertex form

$f(x)+10=2x^{2}-8x$

$f(x)+10=2(x^{2}-4x)$

$f(x)+10+8=2(x^{2}-4x+4)$

$f(x)+18=2(x-2)^{2}$

$f(x)=2(x-2)^{2}-18$ -----> equation in vertex form

The vertex is the point (2,-18)

therefore

The x-component of the vertex is 2

The y-component of the vertex is -18