Graphing Quadratic Equations: Videos & Practice Problems

Which of the following best describes the graph of any quadratic function $y=a{x}^2+bx+c$, with $a\ne 0$?

Given $f\left(x\right)=x^2$, compute $f\left(3\right)$ and explain which point you would plot for $x=3$ on the Cartesian plane.

For the function $y=-\frac{1}{2}{(x+3)}^2+2$, what is the vertex and the equation of the axis of symmetry?

Which equation represents the axis of symmetry for the parabola given by $y=2(x-4{)}^2+1$?

Consider: y = −2(x − 1)² + 3. Which of the following choices correctly describes how this parabola will open and what its width will be compared to y = x²?

Compare the graph of y = 0.25x² to y = x². How is y = 0.25x² different in shape and why?

Starting from f(x) = x², let g(x) = (x − 5)² + 7. Describe the translation of the graph of f to get g and give the vertex of g.

The expression (x + 2)² appears in a quadratic that is written in vertex form. Which statement correctly describes what the horizontal shift will be and why?

Solve $2(x-4{)}^2-18=0$ to find the $x$-intercepts of the parabola.

Does the equation $(x+2{)}^2+5=0$ have real $x$-intercepts? Explain your answer.

Find the x-intercepts of y = 2x² + 12x + 10 using the quadratic formula and state the axis of symmetry.

Which statement correctly interprets the value of the discriminant $D=b^2-4ac$ for a quadratic equation $a{x}^2+bx+c=0$?

What is the $y$-intercept of the quadratic function $y=3x^2-6x+4$?

Convert the quadratic: y = x² − 6x + 5 into vertex form by completing the square, and identify the vertex.

Use the axis-of-symmetry formula $x_v=-\frac{b}{2a}$ to find the vertex of $y=-x^2+4x+1$.

A toy rocket's vertical position, in units of meters, is modeled by: $h\left(t\right)=-5t^2+20t+1$, where $t$ is in seconds. If aerodynamic drag doubles the magnitude of the $t^2$ coefficient, such that the model becomes:$h_2\left(t\right)=-10t^2+20t+1$, determine how the time where the rocket will reach its maximum height and how the maximum height itself will change as a result.

Which of the following statements correctly describes the effect of increasing the constant term $c$ in the standard form: $y=a{x}^2+bx+c$ by $+k$?

Compute the discriminant ($D$) of $3x^2+2x+1=0$ and state the number of real $x$-intercepts.

Given $y=4(x-1{)}^2-8$, identify the vertex of the parabola.

Which combination of features is generally considered sufficient enough to sketch an accurate parabola on graph paper without plotting many additional points?

Expand $y=2(x+3{)}^2-5$ into standard form $y=a{x}^2+bx+c$, and identify $a$, $b$, and $c$.

Solve $\frac{1}{3}(x-6{)}^2-3=0$.

Suppose $y=x^2+bx+3$ has its vertex at $x=-1$. What is the value of $b$?