Question

1. the graph of a quadratic is called __________a. linearb. parabolac. cubicd. smiley face17. $y=x^{2}$ is called the ________ function.a. firstb. lastc. parentd. cubic18. highest point is called the ________ while the lowest point is called the __________solve the system of quadratics (list all solutions)be sure your functions are in “ $y=$ ” form first.19. $x^{2}+y=9$ $y=x^{2}+1$a) (0,1)b) (2,5) (-2,5)c) (2,5) (-2,5) (0,1)d) no solution20. $y=x^{2}-5x+7$$2x-y=-1$

Explanation:

Step1: Q16: Identify quadratic graph shape

The graph of a quadratic function is a parabola.

Step2: Q17: Identify base quadratic function

$y=x^2$ is the parent (base) quadratic function.

Step3: Q18: Define quadratic extrema points

The highest point of a downward-opening parabola is the vertex (maximum), the lowest point of an upward-opening parabola is the vertex (minimum).

Step4: Q19: Substitute $y$ into first equation

Given $y=x^2+1$, substitute into $x^2+y=9$:
$x^2 + (x^2+1) = 9$

Step5: Q19: Simplify and solve for $x$

$2x^2 + 1 = 9$
$2x^2 = 8$
$x^2 = 4$
$x = 2$ or $x = -2$

Step6: Q19: Find corresponding $y$ values

For $x=2$: $y=2^2+1=5$
For $x=-2$: $y=(-2)^2+1=5$

Step7: Q20: Rearrange second equation to $y=$ form

$2x - y = -1 \implies y=2x+1$

Step8: Q20: Set equations equal and solve

$x^2 -5x +7 = 2x +1$
$x^2 -7x +6 = 0$
$(x-1)(x-6)=0$
$x=1$ or $x=6$

Step9: Q20: Find corresponding $y$ values

For $x=1$: $y=2(1)+1=3$
For $x=6$: $y=2(6)+1=13$

Answer:

1. b. parabola
2. c. parent
3. maximum; minimum
4. b) (2,5) (-2,5)
5. (1, 3), (6, 13)