Algebra 1 Unit 7: Quadratic Functions and Equations

Solving quadratics by factoring, square roots and the quadratic formula, the discriminant, vertex form and quadratic models. 12 questions. Have a go at each one on paper before you tap "Show me how".

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Question 1

Solving by factoringNo calculator

Solve $x^2-5x-14=0$.

1. $x=-7 \text{ or } x=2$
2. $x=7 \text{ or } x=2$
3. $x=7 \text{ or } x=-2$
4. $x=14 \text{ or } x=-1$

Question 2

Solving by square rootsNo calculator

Solve $3x^2=75$.

1. $x=5 \text{ or } x=-5$
2. $x=5$
3. $x=\sqrt{72} \text{ or } x=-\sqrt{72}$
4. $x=25 \text{ or } x=-25$

Question 3

Quadratic formulaNo calculator

Use the quadratic formula to find the exact solutions of $x^2-4x-3=0$.

1. $x=3 \text{ or } x=1$
2. $x=2+\sqrt{7} \text{ or } x=2-\sqrt{7}$
3. $x=-2+\sqrt{7} \text{ or } x=-2-\sqrt{7}$
4. $x=2+\sqrt{28} \text{ or } x=2-\sqrt{28}$

Question 4

The discriminantNo calculator

How many real solutions does $2x^2-3x+5=0$ have?

1. No real solutions
2. Two real solutions
3. Infinitely many
4. One real solution

Question 5

VertexNo calculator

What is the vertex of $y=x^2-6x+11$?

1. $(3,11)$
2. $(6,11)$
3. $(-3,2)$
4. $(3,2)$

Question 6

Completing the squareNo calculator

Which expression is $x^2+8x+3$ written in vertex form?

1. $(x+4)^{2}+3$
2. $(x-4)^{2}-13$
3. $(x+8)^{2}-61$
4. $(x+4)^{2}-13$

Question 7

Quadratic modelsNo calculator

A ball's height, in feet, $t$ seconds after it is thrown is $h=-16t^2+64t+5$. What is its greatest height, in feet?

1. $53$
2. $69$
3. $2$
4. $133$

Question 8

Quadratic modelsNo calculator

An object is thrown from a 160-foot cliff. Its height, in feet, after $t$ seconds is $h=-16t^2+48t+160$. After how many seconds does it hit the ground?

1. $2$
2. $5$
3. $10$
4. $3$

Question 9

Axis of symmetryNo calculator

What is the axis of symmetry of $y=2x^2+12x-1$?

1. $x=-3$
2. $x=-6$
3. $x=3$
4. $x=-12$

Question 10

Writing quadraticsNo calculator

Which quadratic has zeros 3 and $-5$ and leading coefficient 1?

1. $x^{2}+2x-15$
2. $x^{2}-2x-15$
3. $x^{2}-15$
4. $x^{2}+8x+15$

Question 11

Quadratic formulaCalculator

What is the positive solution of $x^2+3x-7=0$, to the nearest hundredth?

1. $1.5$
2. $1.55$
3. $1.54$
4. $4.54$

Question 12

Vertex formNo calculator

What is the minimum value of $f(x)=2(x+1)^2-7$?

1. $-1$
2. $1$
3. $7$
4. $-7$