Sapewa

Answered

2021-12-27

a) Determine the x-intercepts of the quadratic equation in both approximate and exact form

b) Determine the vertex point.

c) Determine the y-intercept.

d) Graph the parabola.

Answer & Explanation

Fasaniu

Expert

2021-12-28Added 46 answers

Step 1

Solution: $y={(x+4)}^{2}-7$

${(x+4)}^{2}=y+7$

1) By substituting $y=0$, the x intercept can be achieved.

${(x+4)}^{2}=0+7$

${(x+4)}^{2}=7$

$x+4=\pm \sqrt{7}$

$x=\pm \sqrt{7}-4$

Because of this, x intercepts are $\sqrt{7}-4$ and $-\sqrt{7}-4$

2) contrasting it with the fundamental parabola equation

${(x-h)}^{2}=4a(y-k)$

${(x+4)}^{2}=(y+7)$

$h=-4,{\textstyle \phantom{\rule{1em}{0ex}}}k=-7$

Therefore vertex is $(h,\text{}k)=(-4,\text{}-7)$

Step 2

3) You can get the y intercept by changing $x=0$

$y={(x+4)}^{2}-7$

$y={(0+4)}^{2}-7$

$y=16-7=9$

4) ${(x-h)}^{2}=4a(y-k)$

${(x+4)}^{2}=(y+7)$

$\therefore 4a=1$

$a=\frac{1}{4}$

Therefore four of the parabola is of $(0,\text{}{y}_{4})$

Also $y={(x+4)}^{2}-7$

$y={x}^{2}+16+8x-7$

$y={x}^{2}+8x+9$

Coefficient of $x}^{2}=1\Rightarrow \text{Parabola$ opens up wards.

temzej9

Expert

2021-12-29Added 30 answers

Step 1

Use binomial theorem$(a+b)}^{2}={a}^{2}+2ab+{b}^{2$ to expand $(x+4)}^{2$

$y={x}^{2}+8x+16-7$

Subtract 7 from 16 to get 9.

$y={x}^{2}+8x+9$

Swap sides so that all variable terms are on the left hand side.

${x}^{2}+8x+9=y$

Subtract y from both sides.

${x}^{2}+8x+9-y=0$

This equation is in standard form:$a{x}^{2}+bx+c=0$

Substitute 1 for a, 8 for b, and$9-y$ for c in the quadratic formula, $\frac{-b\pm \sqrt{{b}^{2}-4ac}}{2a}$

$x=\frac{-8\pm \sqrt{{8}^{2}-4(9-y)}}{2}$

Square 8.

$x=\frac{-8\pm \sqrt{64-4(9-y)}}{2}$

Multiply -4 times$9-y$ .

$x=\frac{-8\pm \sqrt{64+4y-36}}{2}$

Add 64 to$-36+4y$ .

$x=\frac{-8\pm \sqrt{4y+28}}{2}$

Take the square root of$28+4y$ .

1)$x=\frac{-8\pm 2\sqrt{y+7}}{2}$

Now solve the equation (1) when$\pm$ is plus. Add -8 to $2\sqrt{7+y}$

$x=\frac{2\sqrt{y+7}-8}{2}$

Divide$-8+2\sqrt{7+y}$ by 2

$x=\sqrt{y+7}-4$

When$\pm$ is minus. Subtract $2\sqrt{7+y}$ by

$x=-\sqrt{y+7}-4$

The equation is now solved

$x=\sqrt{y+7}-4$

$x=-\sqrt{y+7}-4$

Use binomial theorem

Subtract 7 from 16 to get 9.

Swap sides so that all variable terms are on the left hand side.

Subtract y from both sides.

This equation is in standard form:

Substitute 1 for a, 8 for b, and

Square 8.

Multiply -4 times

Add 64 to

Take the square root of

1)

Now solve the equation (1) when

Divide

When

The equation is now solved

karton

Expert

2022-01-09Added 439 answers

Step 1

a) Write the equation in standard form

Step 2

Substitute the values of a, b, and c into the quadratic formula

Step 3

Simplify the discriminant

Step 4

Simplify

Step 5

b) Let's focus on:

Expand the expression

Step 6

Group like terms together

Step 7

Add or subtract the numbers

c) Parabola equation in polynomial form

The vertex ofan up-down facing parabola of the form

Rewrite

The parabola params are:

Simplify

Plug in

Therefore the parabola vertex is

(-4, -7)

If a<0, then the vertex is a maximum value

If Pa>0, then the vertex is a minimum value

Minimum (-4, -7)

Step 8

Most Popular Questions