Quadratics in Standard Form Warmup 5

Find the axis of symmetry for

f(x) = x²- 8x + 15.

• x = -8

• x = 4

• y = 8

• y = -4

Answer explanation

The axis of symmetry for a quadratic function in the form f(x) = ax^2 + bx + c is given by x = -b/(2a). Here, a = 1 and b = -8, so x = -(-8)/(2*1) = 4. Thus, the axis of symmetry is x = 4.

Find the vertex of 
f(x) = -x² - 4x + 12.

• (-2, 16)

• (2, 0)

• (2, 4)

• (-2, 4)

Answer explanation

To find the vertex of the quadratic function f(x) = -x^2 - 4x + 12, use the vertex formula x = -b/(2a). Here, a = -1 and b = -4, giving x = -2. Substitute x = -2 into f(x) to get f(-2) = 16. Thus, the vertex is (-2, 16).

Graph the quadratic.

• A

• B

• C

• D

Answer explanation

The correct graph of the quadratic is choice B, as it accurately represents the parabolic shape and vertex position based on the given quadratic equation. The other options do not match the characteristics of the quadratic.

Tags

CCSS.HSF-IF.C.7A

What is the green dot on the parabola called?

• maximum

• minumum

• roots

• zeros

Answer explanation

The green dot on the parabola represents the maximum point, where the curve reaches its highest value. This is why the correct answer is 'maximum', as it indicates the peak of the parabola.

Tags

CCSS.HSF-IF.C.7A

• up

• down

Answer explanation

The graph of the quadratic function opens down because the coefficient of the x^2 term is negative (-3). Therefore, the correct answer is 'down'.

Tags

CCSS.HSF-IF.C.7A

What is a axis of symmetry?

• all real numbers

• y=5

• the line that divides the graph in equal halves

• y=mx+b

Answer explanation

The axis of symmetry is the line that divides the graph into two equal halves, reflecting it perfectly on either side. This is why the correct answer is 'the line that divides the graph in equal halves'.

Identify a, b, and c if y = -8+3x²+5x

• a=3, b=5, c=-8

• a=-8, b=3, c=5

• a=3x², b=5x, c=-8

• a=3x² , b=-8, c=5x

Answer explanation

In the equation y = -8 + 3x² + 5x, the coefficients are identified as follows: a = 3 (coefficient of x²), b = 5 (coefficient of x), and c = -8 (constant term). Thus, the correct choice is a=3, b=5, c=-8.