Question

PLEASE HELP!!!!

Answer 1

NOTES:

Given a quadratic function in standard format (y = ax² + bx + c), the direction of the parabola is as follows:

• if "a" is positive, then opens UP
• if "a" is negative, then opens DOWN

Given a quadratic function in standard format (y = ax² + bx + c), the vertex can be found as follows:

• the Axis Of Symmetry (x-value) is: x = $\frac{-b}{2a}$  
• y-value is found by plugging in the AOS for "x" in the equation

****************************************************************************************

1) y = x² + 11x + 24

• a = +1 so the parabola opens UP

• x = $\frac{-b}{2a}$ = $\frac{-11}{2(1)}$  = $-\frac{11}{2}$

• y = $(-\frac{11}{2})^{2}$ + 11$(-\frac{11}{2} )$ + 24 = $-\frac{25}{4}$

• vertex $(-\frac{11}{2}$, $-\frac{25}{4})$ is in Quadrant 3 and is below the x-axis

This COULD be the graph of the rain gauge.

The graph should contain the vertex, x-intercepts (-3, 0) and (-8, 0), and y-intercept (0, 24)

******************************************************************************************

2) y = -x² - 6x - 8

• a = -1 so the parabola opens DOWN

• x = $\frac{-b}{2a}$ = $\frac{-(-6)}{2(-1)}$  = $\frac{6}{-2}$ = -3

• y = -(-3)² - 6(-3) - 8 = -9 + 18 - 8 = 1

• vertex (-3, 1) is in Quadrant 2 and is above the x-axis

This could NOT be the graph of the rain gauge.

The graph should contain the vertex, x-intercepts (-2, 0) and (-4, 0), and y-intercept (0, -8)

******************************************************************************************

3) y = x² - 2x + 3

• a = 1 so the parabola opens UP

• x = $\frac{-b}{2a}$ = $\frac{-(-2)}{2(1)}$  = $\frac{2}{2}$ = 1

• y = (1)² - 2(1) + 3 = 1 - 2 + 3 = 2

• vertex (1, 2) is in Quadrant 1 and is above the x-axis

This could NOT be the graph of the rain gauge.

The graph should contain the vertex, y-intercept (0, 3), and its mirror image (2, 3). There are no x-intercepts

******************************************************************************************

4) y = x² + 4x + 4

• a = 1 so the parabola opens UP

• x = $\frac{-b}{2a}$ = $\frac{-4}{2(1)}$  = -2

• y = (-2)² + 4(-2) + 4 = 4 - 8 + 4 = 0

• vertex (-2, 0) is in Quadrant 2 and is on the x-axis

This COULD be the graph of the rain gauge.

The graph should contain the vertex, y-intercept (0, 4), and its mirror image (-4, 4). The x-intercept is the vertex.

Compared to the other four graphs, this is most likely the equation for the rain gauge!

******************************************************************************************

5) y = 3x² + 21x + 30

• a = +3 so the parabola opens UP

• x = $\frac{-b}{2a}$ = $\frac{-21}{2(3)}$  = $-\frac{7}{2}$

• y = 3$(-\frac{7}{2})^{2}$ + 21$(-\frac{7}{2} )$ + 30 = $-\frac{27}{4}$

• vertex $(-\frac{7}{2}$, $-\frac{27}{4})$ is in Quadrant 3 and is below the x-axis

This COULD be the graph of the rain gauge.

The graph should contain the vertex, x-intercepts (-2, 0) and (-5, 0), and y-intercept (0, 30)

*******************************************************************************************

Answer 2

Answer:

this is for the other person sorry it wasnt sooner just found this.

Step-by-step explanation: