help meeeeeeeeeeeee

Question

with this Part 1: Multiple Choice

Find the discriminant of each quadratic equation then state the number and type of solutions.

1) $7 x^{2}-9 x=0$

2) $6 n^{2}+8 n+3=0$

A) 81 ; two real solutions

A) $-87$; two imaginary solutions

B) 121 ; two real solutions

B) $-8$; two imaginary solutions

C) 296 ; two real solutions

C) $-8$; two real solutions

D) 81 ; one real solution

D) 84 ; two real solutions

3) $2 x^{2}+8 x+8=0$

4) $-5 x^{2}-10 x-5=0$

A) 0 ; two imaginary solutions

A) $-175$; two imaginary solutions

B) 0 ; one real solution

B) 200 ; two real solutions

C) 65 ; two real solutions

C) 0 ; one real solution

D) 0 ; two real solutions

D) 0 ; two imaginary solutions

5) $\mathrm{f}(\mathrm{x})=x^{2}$ and $\mathrm{g}(\mathrm{x}) \mathrm{i}=(x+4)^{2}$, then $\mathrm{g}(\mathrm{x})$ is $\quad$ 6) $\mathrm{f}(\mathrm{x})=x^{2}$ and $\mathrm{g}(\mathrm{x})$ is $5 x^{2}$, then $\mathrm{g}(\mathrm{x})$ is $\mathrm{f}(\mathrm{x})$

$\mathrm{f}(\mathrm{x})$ shifted with $\mathrm{a}$

A) up 4

B) right 4

A) none of these

C) left 4

D) down 4

B) different vertex

C) vertical stretch

D) vertical compression

7) $\mathrm{f}(\mathrm{x})=x^{2}$ and $\mathrm{g}(\mathrm{x})$ is $x^{2}+4$, then is $\mathrm{f}(\mathrm{x})$

8) $\mathrm{f}(\mathrm{x})=x^{2}$ and $\mathrm{g}(\mathrm{x})$ is $(1 / 2) x^{2}$, then $\mathrm{g}(\mathrm{x})$ is shifted

A) left 4

B) down 4

C) right 4

D) up 4

A) vertical compression

B) none of these

C) different vertex

D) vertical stretch Part 2: Free Response (Write your answers on your paper)

Fill in the blanks.

9) $f(x)=-x^{2}+4 x-3$

10) $f(x)=2 x^{2}-12 x+16$

$x$ intercept(s)

axis of

symmetry

x intercept(s) axis of symmetry

State the vertex of each function, and the value of a, and which way the parabola of

State the vertex of each function, and the value of a, and which way the parabola opens (up or down).

11) $y=(x+4)^{2}+1$

Vertex

12) $y=(x-3)^{2}+2$

Value of a

Opens

13) $y=2 x^{2}+16 x+34$

Vertex

Vertex

Value of a

Opens

Vertex

Value of $a$ 14) $y=-x^{2}-2 x-4$ Value of $\mathrm{a}$

Opens

15) A golf ball is thrown off of the roof of a building. It's height $h(t)$ after $t$ seconds is modeled

the function $h(t)=-5 t^{2}+4 t+18$

What is the initial height of the golf ball?

Opens

15) A golf ball is thrown off of the roof of a

Answer 1

7x^2 -9x = 0

a=7, b =-9, c = 0

discriminant = b^2 -4ac = 81-28(0)= 81>0

if it's greater than zero, then there's 2 real solutions or 1 with multiplicity 2

in this case it's 2 real solutions.

using the quadratic formula

x = 9/14 + or - (1/14)sqr81 = 9/14 + or - 9/14 = 0 or 18/14=9/7

or you could have just factored 7x^2 -9x to (x)(7x-9) and set each factor = 0

to get x = 0 and x = 9/7

skipping 2) through 14)

15) initial height is the constant term 18 meters