HPC 1-1 Preview Day 2 Notes

HPC 1-1 Preview Day 2 Notes

Review quadratic functions and factoring

Quadratic Function

• Standard form:  $y=ax^2+bx\ +c$  

   $Vertex\ \left(-\frac{b}{2a},\ output\right),\ Axis\ of\ symmetry:\ x\ =\ -\frac{b}{2a}$  

• Vertex form:  $y=a\left(x-h\right)^2+k$  ; Vertex (h, k),                             Axis of symmetry: x = h

• Quadratic formula:  $x=\frac{\left(-b\pm\sqrt{b^2-4ac}\right)}{\left(2a\right)}$  

• Completing the square:  $x^2+bx+\left(\frac{b}{2}\right)^2$  

• When a is +, it is concave up or opens up.

• When a is negative, it is concave down or opens down.

Multiple Choice

Solve by factoring.

2x² - 9x - 35 = 0

• x = 7/2, x = -6

• x = -5/2, x =5

• x = -3/7, x =6

• x = -5/2, x = 7

Multiple Choice

Find the vertex of

f(x) = -x² - 4x + 12

• (-2, 16)

• (2, 0)

• (2, 4)

• (-2, 4)

Multiple Choice

What is the axis of symmetry for the following equation?
y=4x²-8x+9

• x=-8
• x=1
• x=-1
• x=2

Multiple Choice

What are the
x-intercepts of the function
f(x)= (x - 2)(x + 3)?

• x = - 2 or x = 3
• x = 2 or x = -3
• The are no real roots
• x = 2 or x = 3

Multiple Choice

Convert the equation into standard form:

y = -5(x + 2)² - 10

• y = -5x² - 20x - 30

• y = -5x² - 4x - 10

• y = 25x² + 100x + 90

• y = 25x² - 10x - 30

Multiple Choice

Convert the equation

f(x) = x² - 12x + 40

into vertex form

• f(x) = (x + 6)² - 4

• f(x) = (x + 6)² + 4

• f(x) = (x - 6)² - 4

• f(x) = (x - 6)² + 4

Multiple Choice

Use the quadratic formula to find the solutions for
y = 2x² - 9x + 5

• -8.14 and -6.14
• 4.07 and 3.07
• 3.85 and 0.65
• ZERO solutions

Open Ended

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